Fast solution of mixed-potential time-domain integral equations for half-space environments

A fast Fourier transform-accelerated integral-equation based algorithm to efficiently analyze transient scattering from planar perfect electrically conducting objects residing above or inside a potentially lossy dielectric half-space is presented. The algorithm requires O(N_tN_s(log N_s + log² N_t)) CPU and O(N_tN _s) memory resources when analyzing electromagnetic wave interactions with uniformly meshed planar structures. Here, N_t and N_s are the numbers of simulation time steps and spatial unknowns, respectively. The proposed scheme is therefore far more efficient than classical time-marching solvers, the CPU and memory requirements of which scale as O(N_t ² N_s²) and O(N_tN_s ²). In the proposed scheme, all pertinent time-domain half-space Green functions are (pre) computed from their frequency-domain counterparts via inverse discrete Fourier transformation. In this process, in-band aliasing is avoided through the application of a smooth and interpolatory window. Numerical results demonstrate the accuracy and efficiency of the proposed algorithm.